Assessment Math R. 14 Multiply using the distributive p Simplify the expression: (2w-5)(-7)

Answer:

We can simplify this expression by using the formula (a + b)(a - b) = a^2 - b^2:

(1 + √10)(1 - √10) = 1^2 - (√10)^2 = 1 - 10 = -9

Therefore,

(1 + √10)(1 - √10) = -9

Now we can multiply by 2:

2(1 + √10)(1 - √10) = 2(-9)

2(1 - 10) = -18

So the final result is -18.

In the following question, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

To find the surface area of the scratching post, we need to add up the surface areas of all the sides.

The scratching post has a rectangular prism shape with dimensions of 10 cm x 10 cm x 90 cm. The bottom is also a 10 cm x 10 cm square.

So the surface area of the post, including the bottom, is:

2(10 cm x 10 cm) + 2(10 cm x 90 cm) + 2(10 cm x 10 cm) = 200 cm^2 + 1800 cm^2 + 200 cm^2 = 2200 cm^2

Therefore, Jordan needs 2200 square centimetres of carpet to cover the surface of the post, including the bottom.

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The equation of the red graph is g(x) = x² + 3.

Option C.

The equation of the red graph can be determined by considering upscaling or transformation on the x - axis.

Since the equation focuses on the function g(x) and not on upscaling in the y-axis, any changes should not affect the x-axis. Therefore, we can eliminate (x - 3)² and (x + 3)² from the options given, since they involve modifying the x-axis.

In conclusion, as the transformation involves increasing the y-values along the y-axis, the correct choice is x² + 3 rather than x² - 3.

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We can conclude that -

The exponential function is of the form -

f(x) = eˣ

Given is to write the exponential growth and exponential decay equation.

{ 1 } -

The general exponential growth equation is -

[tex]$f(x)=a(1+r)^{x}[/tex]

{ 2 } -

The general exponential decay equation is -

[tex]$\frac {dN}{dt}= -\lambda N[/tex]

Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.

Therefore, we can conclude that -

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The equation of the line shown is y = 2x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2

Constant of proportionality, k = 2.

Therefore, the required equation is given by:

y = kx

y = 2x

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Answer:

x-2

Step-by-step explanation:

If you start of with X, you don't know what the value of X is, so you take away two from what we label as X

Answer:

Now, This number is neither a perfect square nor a perfect cube

So, 34 can be evaluated as, 34 = (30 + 4) (15 + 15 + 4)

Here is the evaluated form of 34.

Step-by-step explanation:

is of goggle btw so just change some of the words

The Rational Roots Theorem states that the possible rational roots of a polynomial equation are the factors of the constant term divided by the factors of the leading coefficient. Therefore, the possible rational roots of P(x) are ±1, ±2, ±4, and ±4.

To find the exact roots of P(x), we can use synthetic division. Synthetic division is an efficient way of dividing a polynomial by a number. Using this method, we can determine that there are three roots for P(x): 1, -2, and -3. To verify this, we can evaluate P(x) for each of the three roots and confirm that the result is zero.

We can also use the quadratic formula to find the remaining two roots. Since P(x) is a 5th degree polynomial, the two remaining roots are complex and can be found using the quadratic formula. The complex roots of P(x) are -0.5 ± 0.5i.

In conclusion, the roots of P(x) are 1, -2, -3, -0.5 ± 0.5i. All of these results can be verified by evaluating P(x) and confirming that the result is zero.

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The composite result function ( g o f )(x) in the functions f(x) = x² - 3 and g(x) = 2x - 1 is 2x² - 7.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, set up the composite result function (g o f)(x).

(g o f)(x) = g( f(x) )

g( x )  = 2x - 1

g( f(x) ) = 2( f(x) ) - 1

g( f(x) ) = 2( x² - 3 ) - 1

Now, simplify the function by applying distributive property.

g( f(x) ) = 2( x² - 3 ) - 1

g( f(x) ) = 2 × x² - 2 × 3 - 1

g( f(x) ) = 2x² - 6 - 1

Add -6 and -1

g( f(x) ) = 2x² - 7

Therefore, the function operation ( g  o f ) is 2x² - 7.

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The exact value of cos(5π/12), using the cosine summation identity, is (√6 - √2)/4.

The exact value of cos(5π/12) can be found using the cosine sum identity, which is:

cos(a + b) = cosa · cosb - sina · sin b

In this case, we can rewrite 5π/12 as (π/4) + (π/6) and use the identity:

cos(5π/12) = cos[(π/4) + (π/6)] = cos(π/4) · cos (π/6) - sin(π/4) · sin (π/6)

Using the values of cos(π/4) = √2/2, cos(π/6) = √3/2, sin(π/4) = √2/2, and sin(π/6) = 1/2, we can plug them into the equation:

cos(5π/12) = (√2/2) · (√3/2) - (√2/2) · (1/2) = √6/4 - √2/4 = (√6 - √2)/4

Therefore, the exact value of cos(5π/12) is (√6 - √2)/4.

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By answering the above question, we may state that Shade the region to line the left of the open circle, since x is less than 4.

A line is a geometric object that is infinitely long and has no width, depth, or curvature. A line, which can also exist in two-, three-, and more-dimensional spaces, is therefore a one-dimensional object. A line is often used to refer to a line segment with two points as its endpoints. A line is a flat, one-dimensional object that may extend indefinitely in both directions and has no thickness. The terms "straight line" or "old correct line" are sometimes used to describe a line that has no "wobble" anywhere along its length.

plot the inequality 4x-22<-6 on a number line,

4x - 22 + 22 < -6 + 22

4x < 16

4x/4 < 16/4

x < 4

Plot an open circle at 4 on the number line to indicate that x is not included in the solution set.

Shade the region to the left of the open circle, since x is less than 4.

The resulting graph should look like this:

     ○----------------->

     |  |  |  |  |  |  |

   -∞  -5  -4  -3  -2  -1  0  1  2  3  4  5  6

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Answer: 126

Step-by-step explanation: I belive that is the answer

Just multiplying the amount of possibilities in each category together will give us the total number of meals that can be made using the options provided.

This is known as the Fundamental Counting Principle. Using this principle, the total number of possible meals is:

6 main courses × 4 vegetables × 2 salads × 3 beverages = 144 possible meals

Therefore, there are 144 possible meals that can be made by choosing from the given options.

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The rank of At is the number of linearly independent rows or columns in the matrix. Since At has an inverse for all values of t, the rank of At is 3 for all values of t.

In order to determine the values of t for which At has an inverse, we need to find the determinant of At. If the determinant of At is not equal to 0, then At has an inverse. The determinant of At is given by:

|At| = (1)(5)(-6) + (3)(t)(4) + (2)(2)(7-t) - (4)(5)(2) - (7-t)(t)(1) - (-6)(2)(3)

Simplifying the above expression, we get:

|At| = -30 + 12t + 28 - 14t - 40 - 5t2 + 12

Combining like terms, we get:

|At| = -5t2 - 2t - 30

Setting the determinant equal to 0, we get:

-5t2 - 2t - 30 = 0

Using the quadratic formula, we can find the values of t for which the determinant is equal to 0:

t = (-(-2) ± √((-2)2 - 4(-5)(-30)))/(2(-5))

t = (2 ± √(4 - 600))/(-10)

t = (2 ± √(-596))/(-10)

Since the square root of a negative number is not a real number, there are no real values of t for which the determinant of At is equal to 0. Therefore, At has an inverse for all values of t.

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Answer:

i need more details i cant answer.

The approximate area of Central Park is about 450 square blocks.

The given dimensions of the park stated in the question are

Length of Central Park = 50 blocks

Width of Central Park = 9 blocks

The approximate area of Central Park is the product of its length and width:

So, we have

Area of Central Park = Length x Width

When the given values are substituted into the the equation mentioned above, we obtain the subsequent expression

Area = 50 * 9

Evaluate

Area = 450

Hence, the approximate area is about 450 square blocks.

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Answer:

Step-by-step explanation:

As before, I'll put slope-intercept first:

5. y = 1/4x + 1 ; y-2 = 1/4(x-4)

6. y = -1/2x + 2 ; y-1 = -1/2(x-2)

7. y = 1/3x + 1 ; y-2 = 1/3(x-3)

8. y = -x ; y-1 = 1(-x+1)

9. y = 2/3x -1 ; y-1 = 2/3(x-3)

Hope this helps!

Answer:

Step-by-step explanation:

Prism:
- Minimum number of faces: 5 (2 bases and 3 lateral faces)
- Minimum number of edges: 9 (3 edges on each base and 3 lateral edges)

Pyramid:
- Minimum number of faces: 4 (1 base and 3 lateral faces)
- Minimum number of edges: 6 (3 edges on the base and 3 lateral edges)

Polyhedron:
- Minimum number of faces: 4 (a tetrahedron)
- Minimum number of edges: 6 (a tetrahedron)

a. A prism is a polyhedron with two parallel congruent bases and rectangular faces connecting the bases. The minimum number of faces for a prism is 5: two bases and three rectangular faces. The minimum number of edges for a prism is 9: three edges connecting each vertex of one base to the corresponding vertex of the other base, and six edges connecting the vertices of the rectangular faces to the vertices of the bases.

b. A pyramid is a polyhedron with a polygonal base and triangular faces connecting the base to a common vertex. The minimum number of faces for a pyramid is 4: one polygonal base and three triangular faces. The minimum number of edges for a pyramid is 6: one edge for each side of the polygonal base, and three edges connecting each vertex of the base to the common vertex.

c. A polyhedron is a three-dimensional shape with flat faces and straight edges. The minimum number of faces and edges for a polyhedron depends on the specific shape, and there is no general formula to determine the minimum values. For example, a tetrahedron has 4 triangular faces and 6 edges, while a cube has 6 square faces and 12 edges. The minimum number of faces and edges for a polyhedron can be calculated by examining the shape and its properties, such as symmetry and number of vertices.

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The marginal profit at a production level of 40 items is 2064.

To find the marginal profit at a production level of 40 items, we need to first find the marginal cost and marginal revenue at this production level. The marginal cost and marginal revenue are the derivatives of the cost and revenue functions, respectively.

The marginal cost function is:
C'(q) = 3q^2 - 22q + 56

The marginal revenue function is:
R'(q) = -6q + 2600

At a production level of 40 items, the marginal cost is:
C'(40) = 3(40)^2 - 22(40) + 56 = 296

The marginal revenue at this production level is:
R'(40) = -6(40) + 2600 = 2360

The marginal profit is the difference between the marginal revenue and marginal cost:
Marginal profit = 2360 - 296 = 2064

Therefore, the marginal profit at a production level of 40 items is 2064.

Answer :[tex]\boxed{2064}[/tex].

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Answer:

<HDG = 39°

Step-by-step explanation:

Red square is a right angle which mean its a 90°

Those two angle <CDG and <HDG are complementary angle which mean they both add up to 90°

<CDG + <HDG = 90°

51° + (3t+15)° = 90°

Solve for t.

3t + 51 + 15 = 90°

3t + 66 = 90°

3t = 24

t = 8

Plug t = 8 into <HDG to find the measurement.

<HDG = 3t + 15

<HDG = 3*8 + 15

<HDG = 24 + 15

<HDG = 39°

The equation x^(4)+6x^(3)-3x^(2)-24x-4=0 has possible rational roots ± 1, 2, 4, ± 1/2, 1/4.

Given the equation: $x^4+6x^3-3x^2-24x-4=0$

To identify possible rational roots we use Rational Root Theorem which states that:

If a polynomial function with integer coefficients has any rational roots then the numerator must divide the constant term and the denominator must divide the leading coefficient. Let's identify possible rational roots. The constant term is -4 and the leading coefficient is 1. Therefore, the possible rational roots are as follows:± 1, 2, 4± 1/2, 1/4

We use synthetic division to test several possible rational roots in order to identify the roots of the equation.

x−40−3−2−4−4−4−4−2+2-2+2-2+2+2-1+1-1+1-1+1+1+4-2+4-2+4-2+4+0-4+0-4+0-4±1 is the root of the equation since the remainder is zero. Therefore, divide the polynomial by x − 1.x^4+6x^3-3x^2-24x-4 = (x-1)(x^3+7x^2+4x+4x+4) = (x-1)(x^3+7x^2+8x+4)

The roots of the equation are x = 1, -2 ± i, where i = √(-1).

Hence, we have completed the following:

Possible rational roots: ± 1, 2, 4, ± 1/2, 1/4

Synthetic division to test possible rational roots: x−40−3−2−4−4−4−4−2+2-2+2-2+2+2-1+1-1+1-1+1+1+4-2+4-2+4-2+4+0-4+0-4+0-4

Possible rational root: ±1

Divide polynomial by (x-1): x^4+6x^3-3x^2-24x-4 = (x-1)(x^3+7x^2+4x+4x+4) = (x-1)(x^3+7x^2+8x+4)

Roots of the equation: x = 1, -2 ± i, where i = √(-1).

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a.  The new interest rate for the loan of $250,000 with 2 points is 5.9%, and the cost of points is $5,000.

b.

The new interest rate for the loan of $260,000 with 3 points is 2.8%, and the cost of points is $7,800.

c.

The new interest rate for the loan of $230,000 with 1 point is 5.09%, and the cost of points is $2,300.

An interest rate is described as the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed.

For part a.

Loan amount = $250,000

Original APR = 6.1%

2 points with a .2% discount per point

Cost of one point = 1% of loan amount = 0.01 x $250,000 = $2,500

Discount per point = 0.2% of loan amount = 0.002 x $250,000 = $500

Total cost of 2 points = 2 x $2,500 = $5,000

Effective interest rate after discount = Original APR - Discount per point = 6.1% - 0.2%

= 5.9%

for part b.

Loan amount = $260,000

Original APR = 3.4%

3 points with a .6% discount per point

Cost of one point = 1% of loan amount = 0.01 x $260,000 = $2,600

Discount per point = 0.6% of loan amount = 0.006 x $260,000 = $1,560

Total cost of 3 points = 3 x $2,600 = $7,800

Effective interest rate after discount = Original APR - Discount per point = 3.4% - 0.6%

= 2.8%

for part c.

c. Loan amount = $230,000

Original APR = 5.6%

1 point with a .51% discount per point

Cost of one point = 1% of loan amount = 0.01 x $230,000 = $2,300

Discount per point = 0.51% of loan amount = 0.0051 x $230,000 = $1,173

Total cost of 1 point = 1 x $2,300 = $2,300

Effective interest rate after discount = Original APR - Discount per point = 5.6% - 0.51%

= 5.09%

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Answer:$7.49

Step-by-step explanation:

just subtract 42.50 from 49.99
49.99-42.50=7.49

Answer:

x = 8

Step-by-step explanation:

4(x + 3) = 44 ( divide both sides by 4 )

x + 3 = 11 ( subtract 3 from both sides )

x = 8

This is the appropriate set notation for the set J, which includes all integers between -5 and -3.

The set J can be rewritten by listing its elements in the appropriate set notation. Since the set J contains all integers between -5 and -3, we can list the elements as follows:

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

J = {-5, -4}

In set notation, this can be written as:

J = {x | x is an integer and -5 <= x < -3}

Therefore, the set J can be rewritten as:

J = {-5, -4}

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The rule for the function g(x) when completed is g(x) = -10, -15 ≤ x < -10; g(x) = -8, -10 ≤ x < -8; g(x) = -6, -8 ≤ x < -1; g(x) = 2, -1 ≤ x < 1; g(x) = 4, 1 ≤ x < 10; g(x) = 8, 10 ≤ x < 15

Given

The graph of the function g(x) such that the function g(x) is a piecewise function and each sub-function is represented by horizontal lines

To complete the function definition, we write out the y value and the domain of the functions based on the current domain

Following the above statements, we have the following function definition for g(x)

g(x) = -10, -15 ≤ x < -10

g(x) = -8, -10 ≤ x < -8

g(x) = -6, -8 ≤ x < -1

g(x) = 2, -1 ≤ x < 1

g(x) = 4, 1 ≤ x < 10

g(x) = 8, 10 ≤ x < 15

The above is the definition of the function g(x)

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Answer:

not a function

Step-by-step explanation:

Answer:

not a function

Step-by-step explanation:

These two numbers are -4, 2. The smallest possible product is -8.

To find a pair of numbers that satisfy the given conditions, we can use algebra. Let x be the first number and y be the second number. According to the problem, one number is 8 less than twice a second number. This can be written as:
x = 2y - 8
We need to find the product of these two numbers, which is x*y. Substituting the value of x from the equation above, we get:
x*y = (2y - 8)*y
= 2y^2 - 8y
To find the smallest possible product, we need to minimize this expression. We can do this by finding the vertex of the parabola represented by this equation. The vertex of a parabola in the form ax^2 + bx + c is given by (-b/2a, f(-b/2a)). In this case, a = 2, b = -8, and c = 0. So, the vertex is:
(-b/2a, f(-b/2a)) = (-(-8)/(2*2), f(-(-8)/(2*2)))
= (2, f(2))
Substituting y = 2 into the equation for the product, we get:
x*y = 2(2)^2 - 8(2)
= 8 - 16
= -8
So, the smallest possible product is -8. To find the pair of numbers that give this product, we can substitute y = 2 into the equation for x:
x = 2y - 8
= 2(2) - 8
= -4
Therefore, the pair of numbers are -4 and 2.

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Answer:

-5 - 2sqrt6

Step-by-step explanation:

To simplify (sqrt2+sqrt3)/(sqrt2-sqrt3), we can rationalize the denominator, which involves multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of sqrt2-sqrt3 is sqrt2+sqrt3, so we can multiply both the numerator and denominator by sqrt2+sqrt3:

(sqrt2+sqrt3)/(sqrt2-sqrt3) * (sqrt2+sqrt3)/(sqrt2+sqrt3) = ((sqrt2+sqrt3)(sqrt2+sqrt3))/((sqrt2-sqrt3)(sqrt2+sqrt3))

Expanding the numerator and simplifying, we get:

(sqrt2+sqrt3)^2 / (sqrt2^2 - sqrt3^2)

= (2 + 2sqrt2sqrt3 + 3) / (2 - 3)

= (5 + 2sqrt6) / (-1)

= -5 - 2sqrt6

Therefore, (sqrt2+sqrt3)/(sqrt2-sqrt3) simplifies to -5 - 2sqrt6.

The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).

We have,

To simplify the expression (√2 + √3) / (√2 - √3), we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.

The conjugate of (√2 - √3) is (√2 + √3).

Multiplying the numerator and denominator by (√2 + √3), we get:

[(√2 + √3) x (√2 + √3)] / [(√2 - √3) x (√2 + √3)]

Expanding both the numerator and denominator:

[(√2 + √3)(√2 + √3)] / [√2 x √2 - √2 x √3 + √3 x √2 - √3 x √3]

Simplifying:

[2 + 2√2√3 + 3] / [2 - 3]

Combining like terms:

[5 + 2√6] / [-1]

Since the denominator is -1, we can multiply both the numerator and denominator by -1 to simplify further:

[5 + 2√6] / 1

Finally, we have:

(5 + 2√6)

Therefore,

The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).

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